Question: Gabriela is 8 years younger than Vanessa. For the last four years, Vanessa and Gabriela have been going to the same school. Three years ago, Vanessa was 5 times as old as Gabriela. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Vanessa and Gabriela. Let Vanessa's current age be $v$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $v = g + 8$ Three years ago, Vanessa was $v - 3$ years old, and Gabriela was $g - 3$ years old. The information in the second sentence can be expressed in the following equation: $v - 3 = 5(g - 3)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = v - 8$ . Substituting this into our second equation, we get the equation: $v - 3 = 5($ $(v - 8)$ $ -$ $ 3)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v - 3 = 5v - 55$ Solving for $v$ , we get: $4 v = 52$ $v = 13$.